A Direct Closed-Form Solution to General Relative Orientation of Two Stereo Views

Abstract

Recovering the relative geometry of two perspective stereo images is a classical problem in photogrammetry and also a basic problem in computer vision. General relative orientation refers to recovering five relative orientation parameters and two principal distances from pure image measurements. This paper presents a new direct closed-form solution to this problem. The approach recasts the explicit stereo coplanarity equation into an implicit form whose coefficients are solvable via a direct solution from the image measurements. Two principal distances, the relative baseline vector and rotation of two images are then solved successively in closed-form from these coefficients. This direct closed-form solution is useful not only in real-time implementation of stereo vision, but also for providing the approximate values of unknown geometric parameters to high-precision photogrammetry, as well as for direct functional analysis of error propagation.